Families of birth-death processes with similar time-dependent behaviour.

R.B. Lenin, P.R. Parthasarathy, Willem R.W. Scheinhardt, Erik A. van Doorn

Research output: Contribution to journalArticleAcademicpeer-review

16 Citations (Scopus)

Abstract

We consider birth-death processes taking values in N ≡ {0,1,... }, but allow the death rate in state 0 to be positive, so that escape from N is possible. Two such processes with transition functions { pij(t) } and { ̃pij(t) } are said to be similar if, for all i, j ∈ N, there are constants cij such that ̃pij(t) = cijpij(t) for all t ≥ 0. We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family. These issues are also resolved in the more general setting in which the two processes are called similar if there are constants cij and ν such that ̃pij(t) = cijeνtpij(t) for all t ≥ 0.
Original languageUndefined
Article number10.1239/jap/1014842840
Pages (from-to)835-849
Number of pages14
JournalJournal of applied probability
Volume2000
Issue number37
DOIs
Publication statusPublished - 2000

Keywords

  • invariant vector
  • EWI-12851
  • transition function
  • METIS-140634
  • Transient behaviour
  • IR-62348
  • Chain sequence
  • Absorption probability

Cite this

@article{2b50bb5419bb4ecca49d0dd0f38ea105,
title = "Families of birth-death processes with similar time-dependent behaviour.",
abstract = "We consider birth-death processes taking values in N ≡ {0,1,... }, but allow the death rate in state 0 to be positive, so that escape from N is possible. Two such processes with transition functions { pij(t) } and { ̃pij(t) } are said to be similar if, for all i, j ∈ N, there are constants cij such that ̃pij(t) = cijpij(t) for all t ≥ 0. We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family. These issues are also resolved in the more general setting in which the two processes are called similar if there are constants cij and ν such that ̃pij(t) = cijeνtpij(t) for all t ≥ 0.",
keywords = "invariant vector, EWI-12851, transition function, METIS-140634, Transient behaviour, IR-62348, Chain sequence, Absorption probability",
author = "R.B. Lenin and P.R. Parthasarathy and Scheinhardt, {Willem R.W.} and {van Doorn}, {Erik A.}",
year = "2000",
doi = "10.1239/jap/1014842840",
language = "Undefined",
volume = "2000",
pages = "835--849",
journal = "Journal of applied probability",
issn = "0021-9002",
publisher = "University of Sheffield",
number = "37",

}

Families of birth-death processes with similar time-dependent behaviour. / Lenin, R.B.; Parthasarathy, P.R.; Scheinhardt, Willem R.W.; van Doorn, Erik A.

In: Journal of applied probability, Vol. 2000, No. 37, 10.1239/jap/1014842840, 2000, p. 835-849.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Families of birth-death processes with similar time-dependent behaviour.

AU - Lenin, R.B.

AU - Parthasarathy, P.R.

AU - Scheinhardt, Willem R.W.

AU - van Doorn, Erik A.

PY - 2000

Y1 - 2000

N2 - We consider birth-death processes taking values in N ≡ {0,1,... }, but allow the death rate in state 0 to be positive, so that escape from N is possible. Two such processes with transition functions { pij(t) } and { ̃pij(t) } are said to be similar if, for all i, j ∈ N, there are constants cij such that ̃pij(t) = cijpij(t) for all t ≥ 0. We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family. These issues are also resolved in the more general setting in which the two processes are called similar if there are constants cij and ν such that ̃pij(t) = cijeνtpij(t) for all t ≥ 0.

AB - We consider birth-death processes taking values in N ≡ {0,1,... }, but allow the death rate in state 0 to be positive, so that escape from N is possible. Two such processes with transition functions { pij(t) } and { ̃pij(t) } are said to be similar if, for all i, j ∈ N, there are constants cij such that ̃pij(t) = cijpij(t) for all t ≥ 0. We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family. These issues are also resolved in the more general setting in which the two processes are called similar if there are constants cij and ν such that ̃pij(t) = cijeνtpij(t) for all t ≥ 0.

KW - invariant vector

KW - EWI-12851

KW - transition function

KW - METIS-140634

KW - Transient behaviour

KW - IR-62348

KW - Chain sequence

KW - Absorption probability

U2 - 10.1239/jap/1014842840

DO - 10.1239/jap/1014842840

M3 - Article

VL - 2000

SP - 835

EP - 849

JO - Journal of applied probability

JF - Journal of applied probability

SN - 0021-9002

IS - 37

M1 - 10.1239/jap/1014842840

ER -